Effective Field Theories can describe physics beyond the Standard Model in a generic way. Their construction is algorithmic, but very cumbersome. In this project, you will learn the concepts of Effective Field Theories and contribute to developing an algorithm for their construction. This will be useful for the interpretation of data collected at the LHC and future colliders, in particular in the light of possible new discoveries.

Helpful pre-requisites:

• Affinity to theoretical physics, mathematics, and possibly computer algorithms.

The gradient flow formalism has been suggested in 2010 to facilitate practical calculations in Lattice QCD. It has proven to be accessible also in perturbation theory and provides a promising link between the two approaches to strong interactions. In this project, you are going to develop means to calculate the resulting Feynman integrals in a systematic way.

The student will learn:

• The general method of the gradient flow.
• Approaches to calculating non-standard Feynman integrals.

Requirements:

• Affinity to mathematics and theoretical physics.

Feynman diagrams provide a very algorithmic way to generate and represent processes in particle physics. In this project, you will devise a generalization of the parlor game Scrabble to Feynman diagrams.

The student will learn:

• The algorithmic structure of Feynman diagrams.

Requirements:

• Interest in Feynman diagrams.
• Affinity to computer programming.

In quantum field theory, the chirality of fermions is implemented by means of projectors in the spinor space containing a tensor named γ₅. When moving from 4 to D dimensions, no natural generalization of chirality exists, and different schemes (i.e. consistent redefinitions of γ₅) may be employed to perform calculations. The implementation of such schemes in an automated computer code represents a valuable asset for modern phenomenological computations.

What to do

• Getting familiar with the concept of fermions and chirality in quantum field theory, as well as with the Kreimer scheme
• Write a computer code that applies the Kreimer scheme to a given amplitude and properly resolves Levi-Civita pseudotensors
• Apply the program to the computation of a cross section

Helpful prerequisites:

• Interest in theoretical physics.
• Basic computing skills.